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On Computing the Resultant of a Polynomial and an Entire Function

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Abstract

Based on Newton’s recurrence formulas on the complex plane, the sums of values of one entire function at zeros of another entire function are found. This allows one to determine whether these functions have common zeros or not. An algorithm for computing an approximation to the resultant of a polynomial (or an entire function with a finite number of zeros) and an entire function is presented. The algorithm is implemented in the Maple computer algebra system. Examples that illustrate the operation of the algorithm are considered.

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Funding

This work was carried out with the support of the following institutions: the first author was supported by the Russian Foundation for Basic Research, the Government of the Krasnoyarsk Krai, and the Krasnoyarsk Regional Science Foundation, grant no. 20-41-243002 (algorithm development and testing); the second author was supported by the Krasnoyarsk Mathematical Center and was financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education, agreement no. 075-02-2021-1388 (development and software implementation of the algorithm); and the third author was supported by the Russian Foundation for Basic Research, grant no. 19-31-60012 (formulation of the requirement specifications for the algorithm and computation of the examples).

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Authors and Affiliations

  1. Siberian Federal University, pr. Svobodnyi 79, 660041, Krasnoyarsk, Russia

    V. I. Kuzovatov & A. A. Kytmanov

  2. Institute of Computational Modeling, Siberian Branch, Russian Academy of Sciences, Akademgorodok 50/44, 660036, Krasnoyarsk, Russia

    E. K. Myshkina

Authors
  1. V. I. Kuzovatov
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  2. A. A. Kytmanov
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  3. E. K. Myshkina
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Corresponding authors

Correspondence to V. I. Kuzovatov, A. A. Kytmanov or E. K. Myshkina.

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The authors declare that they have no conflicts of interest.

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Translated by Yu. Kornienko

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Kuzovatov, V.I., Kytmanov, A.A. & Myshkina, E.K. On Computing the Resultant of a Polynomial and an Entire Function. Program Comput Soft 48, 59–64 (2022). https://doi.org/10.1134/S0361768822010066

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  • DOI: https://doi.org/10.1134/S0361768822010066

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